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Radio-Frequency Capacitive Gate-based Sensing for Silicon CMOS Quantum Electronics

Ahmed, Imtiaz

Published Nov 10, 2018• 2 citations
Publisher

Abstract

This thesis focuses on implementing radio frequency (rf) reflectometry techniques for dispersive detection of charge and spin dynamics in nanoscale devices. I have investigated three aspects of rf reflectometry using state-of-the-art silicon (Si) complementary metal-oxide-semiconductor (CMOS) nanowire field effect transistors (NWFETs). First, a high-sensitivity capacitive gate-based charge sensor is developed by optimising the external matching circuit to detect capacitive changes in the high frequency resonator. A new circuit topology is used where superconducting niobium nitride (NbN) inductor is connected in parallel with a single-gate Si NWFET resulting in resonators with loaded Q-factors in the 400-800 range. For a resonator operating at 330 MHz, I have achieved a charge sensitivity of 7.7 $\mu e/\sqrt{\text{Hz}}$ and, when operating at 616 MHz, I get 1.3 $\mu e/\sqrt{\text{Hz}}$. This gate-based sensor can be used for fast, accurate and scalable techniques for quantum state readout in Si CMOS based quantum computing. Second, this new circuit topology for the resonator is used with a dual-gate Si NWFET. This dual-gate device geometry provides access to a double quantum dot (DQD) system in few electron regime. The spin-state of the two-electron DQD system is detected dispersively using Pauli spin blockade between joint singlet S(2,0) and triplet T$_-$(1,1) states in a finite magnetic field $B$. The singlet-triplet relaxation time $T_1$ at $B=4.5$~T is measured to be $\sim$1 ms using standard homodyne detection technique. Third, I expand the range of applications of gate-based sensing to accurate temperature measurements. I have experimentally demonstrated a primary thermometer by embedding a single-gate Si NWFET with the rf capacitive gate-based sensor. The thermometer, termed as gate-based electron thermometer (GET), relies on cyclic electron tunneling between discrete energy levels of a quantum dot and a single electron reservoir in the NWFET. I have found that the full-width-half-maximum (FWHM) of the resonator phase response depends linearly with temperature via well known physical law by using the ratio $k_\text{B}/e$ between the Boltzmann constant and the electron charge. The GET is also found to be magnetic field independent like other primary thermometers such as Coulomb blockade and shot noise thermometers.

DOI
10.17863/cam.32304

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This thesis focuses on implementing radio frequency (rf) reflectometry techniques for dispersive detection of charge and spin dynamics in nanoscale devices. I have investigated three aspects of rf reflectometry using state-of-the-art silicon (Si) complementary metal-oxide-semiconductor (CMOS) nanowire field effect transistors (NWFETs). First, a high-sensitivity capacitive gate-based charge sensor is developed by optimising the external matching circuit to detect capacitive changes in the high frequency resonator. A new circuit topology is used where superconducting niobium nitride (NbN) inductor is connected in parallel with a single-gate Si NWFET resulting in resonators with loaded Q-factors in the 400-800 range. For a resonator operating at 330 MHz, I have achieved a charge sensitivity of 7.7 μe/Hz\mu e/\sqrt{\text{Hz}}μe/Hz​ and, when operating at 616 MHz, I get 1.3 μe/Hz\mu e/\sqrt{\text{Hz}}μe/Hz​. This gate-based sensor can be used for fast, accurate and scalable techniques for quantum state readout in Si CMOS based quantum computing. Second, this new circuit topology for the resonator is used with a dual-gate Si NWFET. This dual-gate device geometry provides access to a double quantum dot (DQD) system in few electron regime. The spin-state of the two-electron DQD system is detected dispersively using Pauli spin blockade between joint singlet S(2,0) and triplet T−_-−​(1,1) states in a finite magnetic field BBB. The singlet-triplet relaxation time T1T_1T1​ at B=4.5B=4.5B=4.5~T is measured to be ∼\sim∼1 ms using standard homodyne detection technique. Third, I expand the range of applications of gate-based sensing to accurate temperature measurements. I have experimentally demonstrated a primary thermometer by embedding a single-gate Si NWFET with the rf capacitive gate-based sensor. The thermometer, termed as gate-based electron thermometer (GET), relies on cyclic electron tunneling between discrete energy levels of a quantum dot and a single electron reservoir in the NWFET. I have found that the full-width-half-maximum (FWHM) of the resonator phase response depends linearly with temperature via well known physical law by using the ratio kB/ek_\text{B}/ekB​/e between the Boltzmann constant and the electron charge. The GET is also found to be magnetic field independent like other primary thermometers such as Coulomb blockade and shot noise thermometers.
Spin qubits in gate-defined semiconductor quantum dots are a promising platform for realising a scalable quantum computer. This platform encodes quantum information into the intrinsic angular momentum (spin) of individual electrons or holes. In particular, hole spins in quantum dots enable the possibility of all-electrical spin control due to their intrinsic spin-orbit coupling. One important criterion of a quantum computer is the ability to reliably read out the state of the qubit. This is done by mapping spin information to the charge degree of freedom, combined with a method for charge detection. Charge detection can be facilitated by coupling a resonator directly to the quantum dot gate or to a charge sensor and measuring the resonator's phase or amplitude response. In this thesis, we describe a set of experiments relating to the implementation of hole spin qubit readout with superconducting resonators. First, we study gate-based charge sensing in a Si fin field-effect transistor (finFET) device using a superconducting NbN nanowire resonator. We find that the resonator amplifies capacitive crosstalk when electrical control pulses are applied to gate electrodes in this device. This occurs whenever a spectral component of qubit control pulses overlaps with the resonance frequency, which we show may occur for both baseband and radio-frequency (RF) drive signals. We quantify this crosstalk in a transport-based method, and attribute its source to the capacitance between the bondpads of neighbouring gate electrodes. In a second experiment, we use an RF charge sensor with the same nanowire technology to read out hole spin qubits formed in the quantum well of a Ge/SiGe heterostructure. A screening layer approach is used to facilitate RF matching due to large RF dissipation found in the heterostructure. We implement a double-latched readout scheme in this system to reduce errors arising from both spin and charge decay during readout. The spin-to-charge conversion process and its dependence on magnetic field orientation is studied. Spin and charge decay processes arising after spin-to-charge conversion are mitigated by choosing an optimal working point for the field orientation, field amplitude and readout pulse times. By doing so, we achieve an average single-shot state-preparation-and-measurement fidelity of 97%, primarily bounded by imperfect state preparation and limited signal-to-noise ratio. Finally, we study coplanar waveguide resonators fabricated from NbN. We investigate the feasibility of integrating this type of resonator onto the same chip as the Si finFET quantum dots. We then develop a novel resonator readout technique by the interference of two microwave sidebands. We demonstrate the insensitivity of this technique to common-mode phase and amplitude noise both theoretically and experimentally. This technique is then used to study resonator noise arising from two-level system defects. These results highlight both the practical constraints and the potential for achieving high readout fidelities using resonator-based hole spin qubit readout. This work establishes a blueprint for mitigating resonator-induced crosstalk and enabling high-fidelity readout in lossy materials by incorporating a screening layer.
Spins in silicon quantum devices are promising candidates for large-scale quantum computing. Gate-based sensing of spin qubits offers a compact and scalable readout with high fidelity, however, further improvements in sensitivity are required to meet the fidelity thresholds and measurement timescales needed for the implementation of fast feedback in error correction protocols. Here, we combine radio-frequency gate-based sensing at 622 MHz with a Josephson parametric amplifier, that operates in the 500-800 MHz band, to reduce the integration time required to read the state of a silicon double quantum dot formed in a nanowire transistor. Based on our achieved signal-to-noise ratio, we estimate that singlet-triplet single-shot readout with an average fidelity of 99.7% could be performed in 1 μs, well below the requirements for fault-tolerant readout and 30 times faster than without the Josephson parametric amplifier. Additionally, the Josephson parametric amplifier allows operation at a lower radio-frequency power while maintaining identical signal-to-noise ratio. We determine a noise temperature of 200 mK with a contribution from the Josephson parametric amplifier (25%), cryogenic amplifier (25%) and the resonator (50%), showing routes to further increase the readout speed.
Quantum computation requires a qubit-specific measurement capability to read out the final states of individual qubits. Promising semiconductor architectures use external readout electrometers, but these could be replaced by more scalable $g\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}e$ $s\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s$, based on the dispersive coupling between an electrical resonator and the qubit. The authors present an optimized gate sensor and show that significantly better sensitivity arises from changing circuit topology to enhance the resonator's QQQ factor. Here CMOS-based quantum devices achieve charge sensitivity on par with that of the best single-electron electrometers.
Frequency-multiplexed radio-frequency (RF) reflectometry is a promising technique for large-scale quantum dot-based qubit systems because it enables simultaneous readout of multiple qubits and helps to reduce the wiring density in peripheral circuits. However, in the conventional L-C-type matching circuits, resonator frequency tunability is limited by poor design flexibility of the shunt capacitance and hence the circuit. Recently, L-L-type matching circuits comprising a series and a shunt inductor have been proposed to address this issue. Here, we report RF reflectometry readout of silicon quantum dot-based charge sensors embedded in L-L-type circuits. We determine the inductance values for target resonance frequencies based on our equivalent circuit model that incorporates the parasitic elements of the inductors and demonstrate resonator frequency tunability of up to 1 GHz with 3-dB resonator bandwidths on the order of MHz. The measured conductance sensitivities, on the order of 10−5(e2/h)/Hz at 4 K, are only moderately dependent on the resonance frequency up to 630 MHz. These results highlight the prospects of L-L-type matching circuits for rapid and multiplex reflectometry readout of semiconductor spin qubits.
Radio-frequency (RF) reflectometry is widely used for high-bandwidth readout of semiconductor quantum devices at cryogenic temperatures, but its application has mainly been limited to nanoscale structures with relatively small capacitances. Here, we investigate RF readout in a different regime by applying gate-based reflectometry to a large-area silicon carbide transistor with parasitic capacitances orders of magnitude larger than those of typical quantum devices, conditions normally expected to hinder RF readout. We observe a gate-dependent RF response which degrades and eventually vanishes as temperature is lowered, although MOSFET operation in DC transport is maintained down to deep cryogenic temperatures. We attribute this behaviour to impedance changes introduced by carrier freeze-out in the transistor drift region, and propose a modified circuit configuration designed to restore sensitivity under these conditions. These results establish how parasitic pathways and device geometry can limit RF readout, providing insight into the design of scalable cryogenic-CMOS quantum systems.
In gate-based dispersive sensing, the response of a resonator attached to a quantum dot gate is detected by a reflected radio frequency signal. This enables fast readout of spin qubits and tune up of arrays of quantum dots but comes at the expense of increased susceptibility to crosstalk, as the resonator can amplify spurious signals and induce fluctuations in the quantum dot potential. We attach tank circuits with superconducting NbN inductors and internal quality factors Qi>1000 to the interdot barrier gate of silicon double quantum dot devices. Measuring the interdot transition in transport, we quantify radio frequency crosstalk that results in a ring-up of the resonator when neighboring plunger gates are driven with frequency components matching the resonator frequency. This effect complicates qubit operation and scales with the loaded quality factor of the resonator, the mutual capacitance between device gate electrodes, and with the inverse of the parasitic capacitance to ground. Setting qubit frequencies below the resonator frequency is expected to substantially suppress this type of crosstalk.